Q10 of 176 Page 8

If a, b, c are in A.P., prove that:

(a — c)2 = 4 (a — b)(b — c)

Given: a, b, c are in AP


∴ a + c = 2b


…(i)


Now taking RHS i.e. 4(a – b)(b – c)


[from(i)]




⇒(a – c)2


= LHS


Hence Proved


More from this chapter

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8

are in A.P., show that are in A.P. provided a + b + c 0

 9

If (b – c)2, (c – a)2, (a – b)2 are in A.P., then show that: are in A.P.

[Hint: Add ab + bc + ca — a2 — b2 — c2 to each term or let = b — c, = c— a, = a — b, then + + = 0]

 10

If a, b, c are in A.P., prove that:

a3 + c3 + 6abc = 8b3

 10

If a, b, c are in A.P., prove that:

(a + 2b — c)(2b + c — a)(c + a — b) = 4abc


[Hint: Put b = on L.H.S. and R.H.S.]